Color imaging devices use combinations of different colorants to form color images for display or printout on media such as paper or film. Many hardcopy printing devices use combinations of cyan, magenta, yellow, and black (CMYK) to form color imagery. These colorants (or device-dependent coordinates) of C, M, Y and K may correspond to a gamut of colorimetric values that the device is capable of producing. Other devices, such as monitors, may use the colorants red, green, and blue (RGB). Some high-fidelity color imaging devices may use the colorants cyan, magenta, yellow, and black in combination with other colorants such as orange and green. Although there is sometimes a non-linear relationship between device-dependent coordinates and colorants, the terms are used interchangeably in this document.
Device-independent coordinates have been developed to standardize color specification across different devices. For instance, one industry standard that is used to define different color values is the Commission Internationale de l'Eclairage L*a*b* color space (hereafter L*a*b* color space, L*a*b* space, or simply L*a*b*). A point in L*a*b* space defines a color value irrespective of any particular device coordinate. A point in L*a*b* space can be mapped to a point in a device gamut. That point in the device gamut, in turn, may define a combination of device colorants that will produce a color equivalent to that defined by the point in L*a*b* space.
Methods have been developed for converting and mapping device-dependent colorants such as RGB or CMYK into device-independent coordinates such as L*a*b*. FIG. 1 shows a representation of an example device-dependent gamut (e.g., on the left is an example RGB device coordinate gamut) and an example of a device-independent gamut (e.g., on the right is the corresponding L*a*b* coordinate gamut).
In the conversion process, however, if the number of colorants is greater than three, more than one point in a device gamut may be mapped to a single point in L*a*b* space. This presents a problem when converting from L*a*b* to the device-dependent colorants.